ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of Si3N4 (Materials Project id mp-988)

       403      180      105        0        0        0  
       180      403      105        0        0        0  
       105      105      526        0        0        0  
         0        0        0       99        0        0  
         0        0        0        0       99        0  
         0        0        0        0        0      112  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 234.67 GPaEV = 318.02 GPaGV = 124.8 GPaνV = 0.27413
ReussKR = 234.25 GPaER = 299.03 GPaGR = 116.15 GPaνR = 0.28724
HillKH = 234.46 GPaEH = 308.58 GPaGH = 120.48 GPaνH = 0.28064

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
99 GPa 99 GPa 112 GPa 223 GPa 403.3 GPa 705.7 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 268.84 GPa 488.18 GPa 1.3106 TPa–1 1.4792 TPa–1 99 GPa 168.28 GPa0.116520.39187Value
Anisotropy 1.816 1.1287 1.7 3.3631Anisotropy
Axis 0.7967
0.0000
0.6044
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.5000
0.5000
-0.7071
1.0000
0.0002
0.0000
0.4551
0.4551
-0.7654
Axis
-0.7660
0.6428
-0.0000
-0.5001
-0.4999
-0.7071
-0.0000
0.0002
-1.0000
-0.5412
-0.5412
-0.6436
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane